Question

已知m+1/m=3,求m^2-1/m^2的值

Answer 1

解：

(m-1/m)²

=m²+1/m²-2

=m²+1/m²+2-4

=(m+1/m)²-4

=3²-4

=5

所以m-1/m=±√5

于是

m²-1/m²

=(m+1/m)(m-1/m)

=3x(±√5)

=±3√5

Answer 2

m+1/m=3,
两边平方
m^2+1/m^2+2=9
那么m^2+1/m^2=7
两边再平方
m^4+1/m^4+2=49
m^4+1/m^4=47
m^4-2+1/m^4=45
即(m^2-1/m^2)^2=45
m^2-1/m^2=±3√5